As shown by [1]}, the maximisation of the loss over transformations can be written as the semi-infinite constrained optimization problem
\(\max _{g \in \mathcal {G}}\ell \left(f_{\theta }\left(g\mathbf {x}\right), y\right) = & \sup _{\lambda \in \mathcal {L}^2_+} \int _{\mathcal {G}} \lambda (g)\ell (f_{\theta }(g\mathbf {x}), y)dg.\\ \nonumber & \text{s. to} \int _{\mathcal {G}} \lambda (g)dg = 1\;\;\) 
